Topology of the Fermi surface beyond the quantum critical point

2008/06/11 by V. A. Khodel, J. W. Clark, M. V. Zverev · 96 citations
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Critical point (mathematics) #Geometry #Iron-based superconductors research #Mathematics #Physics #Quantum #Quantum critical point #Quantum mechanics #Quantum phase transition #Rare-earth and actinide compounds #Surface (topology) #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.78.075120

published in Physical Review B 78(7) (American Physical Society) · 20 pages, 11 figures

arxiv created 2008/06/11 · openalex publication_date 2008/08/25 · arxiv updated 2010/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We examine the nature of phase transitions occurring in strongly correlated Fermi systems at the quantum critical point (QCP) associated with a divergent effective mass. Conventional scenarios for the QCP involving collective degrees of freedom are shown to have serious shortcomings. Working within the original Landau quasiparticle picture, we propose an alternative topological scenario for the QCP in systems that obey standard Fermi-liquid (FL) theory in advance of the QCP. Applying the technique of Poincar'e mapping, we analyze the sequence of iterative maps generated by the Landau equation for the single-particle spectrum at zero temperature. It is demonstrated that the Fermi surface is subject to rearrangement beyond the QCP. If the sequence of maps converges, a multiconnected Fermi surface is formed. If it fails to converge, the Fermi surface swells into a volume that provides a measure of entropy associated with formation of an exceptional state of the system characterized by partial occupation of single-particle states and dispersion of their spectrum proportional to temperature. Based on this dual scenario, the thermodynamics of Fermi systems beyond the QCP exhibits striking departures from the predictions of standard FL theory. Mechanisms for the release of the entropy excess of the exceptional state are discussed.

Citations

• The break-up of heavy electrons at a quantum critical point
• Metal–insulator transitions and the effects of electron–electron interactions in two-dimensional electron systems
• Curie Law, Entropy Excess, and Superconductivity in Heavy Fermion Metals and Other Strongly Interacting Fermi Liquids
• Metal–insulator transition in two-dimensional electron systems
• Nonvanishing Energy Scales at the Quantum Critical Point ofCeCoIn5
• Ground-state instability in systems of strongly interacting fermions
• Quantum critical phenomena
• Strongly enhanced effective mass in dilute two-dimensional electron systems: System-independent origin
• The multi-connected momentum distribution and fermion condensation
• Thermodynamic spin magnetization of strongly correlated two-dimensional electrons in a silicon inversion layer
• Quantum phase transition in the heavy-fermion compoundYbIr2Si2
• Ferromagnetic Quantum Critical Fluctuations inYbRh2(Si0.95Ge0.05)2